Time and Expected Value of Sample Information Wait for No Patient

Objective:  The expected value of sample information (EVSI) from prospective trials has previously been modeled as the product of EVSI per patient, and the number of patients across the relevant time horizon less those "used up" in trials. However, this implicitly assumes the eligible patient population to which information from a trial can be applied across a time horizon are independent of time for trial accrual, follow-up and analysis.
Methods:  This article demonstrates that in calculating the EVSI of a trial, the number of patients who benefit from trial information should be reduced by those treated outside as well as within the trial over the time until trial evidence is updated, including time for accrual, follow-up and analysis.
Results:  Accounting for time is shown to reduce the eligible patient population: 1) independent of the size of trial in allowing for time of follow-up and analysis, and 2) dependent on the size of trial for time of accrual, where the patient accrual rate is less than incidence. Consequently, the EVSI and expected net gain (ENG) at any given trial size are shown to be lower when accounting for time, with lower ENG reinforced in the case of trials undertaken while delaying decisions by additional opportunity costs of time.
Conclusions:  Appropriately accounting for time reduces the EVSI of trial design and increase opportunity costs of trials undertaken with delay, leading to lower likelihood of trialing being optimal and smaller trial designs where optimal.